Three Problems in Graph Imbedding to Show P Does Not Equal NP

The P versus NP problem, a conjecture formulated by Stephen Cook in 1971, is one of the most challenging problems in contemporary mathematics and theoretical computer science. A concise mathematical formulation of the problem reads: is P = NP? In longer phrasing, this asks: given a problem instance, if some additional data can be recognized fast enough as logically implying the existence of a solution (to the instance), then can a so- lution be computed fast enough? we formulate three problems in graph imbedding to show P ≠ NP.